Ka hana i hana ʻia me ka ikaika
1.1 Wehewehena o ka Hana
Inā ʻoe e paʻi i kahi puke ma luna o ka papaʻaina a hiki i ka wā e neʻe ai ka puke, ua ʻōlelo ʻia ua hana ʻoe i ka hana ma luna o ka puke. Inā hāʻule kahi mea i ka honua ma muli o ka huki ʻana o ka ikaika umekaumaha, ua ʻōlelo ʻia ua hana ka ikaika umekaumaha ma luna o ka mea. I ka ʻaoʻao ʻē aʻe, inā ʻoe e paʻi i kahi mea me kou ikaika a pau a hiki i ka wā e hou nui ai ʻoe, akā ʻaʻole neʻe iki ka mea, ua ʻōlelo ʻia ʻaʻole ʻoe i hana i ka mea. I ke ola o kēlā me kēia lā, hiki i ka poʻe ke ʻōlelo ua hana nui ʻoe ma ka paʻi ʻana i ka mea akā ma ka Physics, ʻaʻole ʻoe e hana ma luna o ka mea no ka mea ʻaʻohe neʻe ʻana o ka mea.
Hiki ke hana ʻia ka hana ma luna o kahi mea e ka ikaika mau (ʻo ka nui a me ke kuhikuhi he mau) a i ʻole ka ikaika loli (ʻo ka nui a me ke kuhikuhi e loli ana). ʻO kahi hiʻohiʻona o ka ikaika me ka nui a me ke kuhikuhi mau he ikaika umekaumaha, e hana ana ma luna o kahi mea ke kokoke ka mea i ka ʻili honua. Ke hāʻule manuahi kahi mea kokoke i ka ʻili honua, ʻo ka nui a me ke kuhikuhi o ka wikiwiki hāʻule manuahi o ka mea he mau no ka mea he mau ka nui a me ke kuhikuhi o ka ikaika umekaumaha e hoʻolalelale ana i ka mea. ʻO kahi hiʻohiʻona o ka ikaika me ka nui mau ʻole (akā me ke kuhikuhi mau) ʻo ia ka ikaika puna . ʻO kekahi laʻana he rocket i hoʻokuʻu ʻia i ka lewa a i ʻole e hoʻi ana i ka ʻili o ka honua. Ke hoʻokuʻu ʻia kahi rocket, e loli ka nui o ka ikaika umekaumaha e hana ana ma luna o ia mea ma kahi ʻāpana kū'ē i ka mamao huinaha mai ke kikowaena o ka honua.
1.1.1 Hana i hana ʻia e nā mana mau
Ma ke ʻano makemakika, ua wehewehe ʻia ka hana i hana ʻia e ka ikaika mau ma luna o kahi mea he neʻe ʻana i hoʻonui ʻia e ka ikaika a i ʻole kahi ʻāpana o ka ikaika nona ke kuhikuhi like me ka neʻe ʻana o ka mea. E nānā i kahi mea ma luna o ka ʻili o kahi mokulele pālahalaha ʻino me ka neʻe ʻana i ka ʻākau i hoʻokumu ʻia e ka ikaika hoʻokuʻi (F).
Kiʻi 1. (Luna) ʻO ke kuhikuhi o ka neʻe ʻana o ka mea ua like ia me ka ikaika F. (Lalo) ʻO ke kuhikuhi o ka neʻe ʻana o ka mea ua like ia me ka ʻāpana o ka ikaika F ma ke kuhikuhi ʻaoʻao (F cos).
ʻO ka hana i hana ʻia e ka ikaika hoʻokuʻu (F):
W = (F)(s)(cos θ) = Fs (cos 0) = Fs (1)
W = Fs
ʻO ka hana i hana ʻia e ka ʻāpana o ka ikaika F ma ke kuhikuhi ʻaoʻao (F cos θ):
W = (F cos θ)(s)(cos 0) = (F cos )(s)(1)
W = Fs cos θ
ʻO ka hana i hana ʻia e ka ikaika frictional kinetic (f k ) penei:
W = (f k )(s)(cos 180) = (f k )(s)(-1)
W = – (f k )(s)
ʻO ka hana i hana ʻia e ka ikaika maʻamau (N):
W = (N)(s)(cos 90) = (N)(s)(0) = 0
ʻO ka hana i hana ʻia e ke kaumaha (w):
W = (w)(s)(cos 90) = (w)(s)(0) = 0
Wehewehe: W = hana, s = ka nui o ka neʻe ʻana, θ = ke kihi ma waena o ka ikaika a me ka neʻe ʻana.
Hōʻike 2.
(a) Ke hāʻule manuahi nei ka mea. Aia ke kaumaha ma ke kuhikuhi like me ka neʻe ʻana (b) Neʻe pololei ka mea i luna. ʻO ke kuhikuhi o ke kaumaha he ʻokoʻa ia i ke kuhikuhi o ka neʻe ʻana.
Ma ke ʻano ma mua, ʻo ka hana i hana ʻia e ke kaumaha (w) he waiwai o ka ʻole no ka mea ʻo ke kuhikuhi o ke kaumaha o ka mea e kū pono ana i ke kuhikuhi o ka neʻe ʻana o ka mea. Pono e hoʻomaopopo ʻia ʻaʻole e loaʻa ka waiwai o ka hana i hana ʻia e ke kaumaha i ka ʻole inā like ke kuhikuhi o ke kaumaha me ke kuhikuhi o ka neʻe ʻana o ka mea a i ʻole kūʻē i ke kuhikuhi.
ʻO ka hana i hana ʻia e ke kaumaha (w) ma luna o ka mea e hāʻule manuahi ana i hōʻike ʻia ma ke kiʻi a penei:
W = Fs (cos θ) = wh (cos 0) = wh (1) = wh = mgh
ʻO ka hana i hana ʻia e ke kaumaha (w) ma luna o ka mea e neʻe ana i luna i luna e like me ka mea i hōʻike ʻia ma ke kiʻi b:
W = Fs (cos θ) = wh (cos 180) = wh (-1) = – wh = – mgh
Wehewehe: w = kaumaha (Newton), h = kiʻekiʻe (mika), m = nuipa (kg), g = wikiwiki o ka umekaumaha (mika no kekona kuea).
Wahi a ka wehewehe ʻana ma mua, ua huki ʻia nā hopena penei: ʻO ka mua, inā ʻaʻole i ʻike kahi mea i kekahi neʻe ʻana, ʻaʻole hana ka ikaika i hoʻokau ʻia ma luna o ka mea. Inā s = 0, W = 0; ʻO ka lua, inā hana kahi ikaika i kahi kihi i hāʻawi ʻia i ka neʻe ʻana o kahi mea, ʻo ka ʻāpana o ka ikaika e kaʻana like ana i ke kuhikuhi like me ka neʻe ʻana o ka mea e hana ma luna o ka mea; ʻO ke kolu, ʻo kahi ikaika ma kahi kuhikuhi e kū pono ana i ke kuhikuhi o ka neʻe ʻana o kahi mea e hana i kahi kihi o 90 o . Cos 90 = 0; ʻO ka hā, hiki i ka hana ke loaʻa kahi hōʻailona maikaʻi a maikaʻi ʻole paha. Inā like ka ikaika me ka neʻe ʻana o ka mea a hana i kahi kihi o 0 o , hana ia i ka hana maikaʻi ma luna o ka mea. I ka ʻaoʻao ʻē aʻe, inā he kuhikuhi ko ka ikaika e kūʻē i ke kuhikuhi o ka neʻe ʻana o ka mea a hana i kahi kihi o 180 o , hana ia i ka hana maikaʻi ʻole ma luna o ka mea.
Kiʻi 3. Kiʻi o ka ikaika (F) - ka neʻe ʻana (s). Ua like ka hana me ka ʻāpana i aka ʻia.
ʻO ka hana i hana ʻia e ka ikaika mau ma luna o kahi mea i ka wā e neʻe ai ka mea ua like ia me ka ʻāpana i aka ʻia ma ka pakuhi ikaika (F) - kūlana (s).
Ua hōʻike ʻia ka hana ma ke ʻano he W (hua nui), a ua hōʻike ʻia ke kaumaha ma ke ʻano he w (hua liʻiliʻi). ʻO ke anakahi SI o ka hana ʻo ia ka Newton ∙ mika (N m). Ua like ia me ka Joule, i hoʻopōkole ʻia ʻo J.
Ua kapa ʻia ʻo ia pēlā no ka hoʻohanohano ʻana i ke kauka Pelekane o ke kenekulia 19 , ʻo James Prescott Joule.
Laʻana nīnau 1: Hana i hana ʻia e ka ikaika mau
Aia kekahi mea ma luna o ka papahele ʻole o ka friction. Hoʻopili ʻia kahi ikaika o 10 N ma luna o ka mea, e hana ana i kahi kihi 30-degere e kūʻē i ka papahele. Inā neʻe ka mea i 1 mika ka mamao, ehia ka hana i hana ʻia e ka ikaika ma luna o ka mea?
pāʻoihana:
ʻIke ʻia: F = 10 N, s = 1 mika
Makemake ʻia: Hana (W)
W = (F)(s)(cos 30 o ) = (10 N)(1 m)(1/2 √ 3) = 5 √ 3 N m
Laʻana nīnau 2: Hana ma o ka ikaika mau
Ke hāʻule manuahi nei kahi niu he 0.2 kg mai ke kiʻekiʻe o 10 mika mai luna o ka honua. Inā he 10 m/s² ka wikiwiki o ka umekaumaha , ehia ka hana i hana ʻia e ke kaumaha ma luna o ka niu?
pāʻoihana:
ʻIke ʻia: m = 0.2 kg, h = 10 m, g = 10 m/s 2
Makemake ʻia: Hana (W) ma ke kaumaha (w)
W = F s = wh = mgh = (0.2 kg)(10 m/s 2 )(10 m) = 20 kg m 2 /s 2 = 20 N m = 20 Joules
1.1.2 Hana ma o nā mana loli
ʻO kahi hiʻohiʻona o ka ikaika loli, ʻo ia ka ikaika puna. Hoʻololi mau ka nui o ka ikaika puna. No laila, ʻaʻole hiki ke helu ʻia ka hana i hana ʻia e ka ikaika puna ma luna o kahi mea me ka hoʻohana ʻana i ke ʻano hana o nā ikaika mau (W = F s cos θ). Inā hoʻolōʻihi ʻia kahi puna, ʻo ka nui o ke hoʻolōʻihi ʻia ʻana o ka puna, ʻo ka nui o ka ikaika tensile e pono ai e hoʻolōʻihi i ka puna. A inā hoʻopaʻa ʻia ka puna, ʻo ka nui o ke hoʻopaʻa ʻia ʻana o ka puna, ʻo ka nui o ka ikaika hoʻokuke e pono ai. Ke hoʻopaʻa ʻia a hoʻolōʻihi ʻia paha ka puna, hoʻololi ka ikaika puna mai 0 (x = 0) a i kahi waiwai kiʻekiʻe loa (F = kx). No laila, ua helu ʻia ka nui o ka ikaika puna me ka hoʻohana ʻana i ka awelika. ʻO ka awelika o ka nui o ka ikaika puna:
ʻO ka hana i hana ʻia e ka ikaika puna ma luna o kahi mea:
W = hana, x = Δx = ʻokoʻa puna (mika), F = ikaika puna (Newton).
Laʻana nīnau 3: Hana ma o kahi ikaika loli
Ma luna o kahi pūnāwai ua kau ʻia ke kaumaha me ka nuipa o 1 kg, no laila e hoʻolōʻihi ʻia ka pūnāwai e 2 cm. Inā he 10 m/s 2 ka wikiwiki o ka umekaumaha , e hoʻoholo (a) ke kūpaʻa pūnāwai (b) ka hana i hana ʻia e ka ikaika pūnāwai ma ke kaumaha.
pāʻoihana:
ʻIke ʻia: m = 1 kg, g = 10 m/s 2 , x = Δx = 2 cm = 0.02 m.
(a) ke kūpaʻa puna
(b) ua hana ʻia ka hana e ka ikaika puna ma luna o ke kaumaha
W = -1/2 kx 2 = -1/2 (500)(0.02) 2 = – (250)(0.0004) = -0.1 Joule
He waiwai maikaʻi ʻole ka hana i hana ʻia e ka ikaika puna ma luna o ke kaumaha no ka mea, ʻo ke kuhikuhi o ka ikaika puna e kūʻē ana i ke kuhikuhi o ka neʻe ʻana o ke kaumaha (aia ka ikaika puna i luna, aia ke kaumaha i lalo).
1.2 Hana Pūnaewele a i ʻole Hana ma o ka Mana Pūnaewele
Inā hoʻokahi wale nō ikaika e hana ana ma luna o kahi mea i ka wā e neʻe ana ka mea, ua like ka hana i hana ʻia e ka ikaika ʻupena me ka hana i hana ʻia e ka ikaika. No ka laʻana, inā hāʻule manuahi kahi mea a hoʻowahāwahā ʻia ka palena o ka ea, ʻo ka ikaika wale nō e hana ana ma luna o ka mea ʻo ia ka ikaika umekaumaha. I kēia hihia, ʻo ka ikaika ʻupena e hana ana ma luna o ka mea ʻo ia ka ikaika umekaumaha (e nānā i ke kiʻi 2).
W ʻupena = W umekaumaha
Inā e hana ana kekahi mau ikaika ma luna o kahi mea i ka wā e neʻe ai ka mea, ua like ka hana i hana ʻia e ka ikaika ʻupena me ka hana ʻupena i hana ʻia e nā ikaika āpau e hana ana ma luna o ka mea (e nānā i ke kiʻi 1).
ʻupena W = W 1 + W 2 + W 3 + W 4
Hiki ke helu ʻia ka hana i hana ʻia e ka ikaika upena ma luna o kahi mea ma ka ʻimi mua ʻana i ka ikaika upena a laila hoʻonui iā ia me ka nui o ka neʻe ʻana.
W = ΣF s
Laʻana nīnau 4: Pūnaewele
Ua paʻi ʻia kahi pahu paʻa ma ka papahele me ka ikaika o 20 N a hiki i ka neʻe ʻana o ka pahu i 1 mika ka mamao. Inā like ka ikaika hoʻokuke me ka neʻe ʻana o ka pahu a hana ka pahu i kahi ikaika frictional kinetic o 2 N, e hoʻoholo i ka nui o ka hana upena i hana ʻia e ka ikaika upena ma ka pahu.
pāʻoihana:
ʻIke ʻia: F = 20 N, f k = 2 N, s = 1 m
W 1 = F s = (20 N)(1 m) = 20 Nm = 20 Joules
W 2 = f k s = – (2 N)(1 m) = – 2 Nm = – 2 Joules
Hana pūnaewele a i ʻole ka hana i hana ʻia e ka ikaika pūnaewele
W upena = W 1 – W 2 = 20 J – 2 J = 18 J
Laʻana nīnau 4) Hana ka ikaika hoʻokuʻi (F) i ka hana maikaʻi, hana ka ikaika frictional kinetic (f k ) i ka hana maikaʻi ʻole
